Why is it important that Hamilton’s equations have the four symplectic properties and what do they mean?

The symplectic properties are: time invariance conservation of energy the element of phase space volume is invariant to coordinate transformations the volume the phase space element is invariant with respect to time I’m most inerested in what 3 and 4 mean and why they are important. Answer Coordinate invariance guarantees that the phase space M … Read more

Is an electron/proton gun possible?

In the 1944 SF story “Off the Beam” by George O. Smith, an electron gun is constructed along the length of a spaceship. In order to avoid being constrained by a net charge imbalance, it is built to also fire the same number of protons in the other direction, dissipating the mass of the “cathode”. … Read more

What are some interesting calculus of variation problems? [closed]

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for … Read more

Uniqueness of eigenvector representation in a complete set of compatible observables

Sakurai states that if we have a complete, maximal set of compatible observables, say A,B,C… Then, an eigenvector represented by |a,b,c….>, where a,b,c… are respective eigenvalues, is unique. Why is it so? Why can’t there be two eigenvectors with same eigenvalues for each observable? Does maximality of the set has some role to play in … Read more

Entanglement and the double slit experiment

Is the double slit experiment an example of entanglement when it seems as if the photon is going through both slits? Or put another way, is it at this stage when we attempt measurement we see a photon on one side affect the photon on the other side? Do entangled particles have to be made … Read more

How to apply an algebraic operator expression to a ket found in Dirac’s QM book?

I’ve been trying to learn quantum mechanics from a formal point of view, so I picked up Dirac’s book. In the fourth edition, 33rd page, starting from this:ξ|ξ′⟩=ξ′|ξ′⟩ (Where ξ is a linear operator and all the other ξ′‘s are eigen-(value|ket)s.) ,and this:ϕ(ξ)=a1ξn+a2ξn−1⋯an=0 (where ϕ is an algebraic expression) He has deduced ϕ(ξ)|ξ′⟩=ϕ(ξ′)|ξ′⟩ I understand … Read more